Inverter Advice Please

SWMB needs to be able to dry her hair when wilding and our travel hair dryer is rated at 1600W according to the blurb. When I look at inverters on Amazon there seems to be a lot of choice around the £25.00 mark but these are only rated at 300W. How do you guys get around this? Do we need a lower power hairdryer or an much more powerful (and expensive) inverter?